In current wireless networks, most algorithms are iterative and might not be able to meet the requirements of some 5G technologies such as ultra-reliable low-latency communication within a very low latency budget. For instance, requiring and end-to-end latency below 1ms, many signal processing tasks must be completed within microseconds. Therefore, only a strictly limited number of iterations can be performed, which may lead to uncontrollable excessive errors. We argue in favor of formulating the underlying optimization problems as convex feasibility problems in order to enable massively parallel processing on GPUs for online learning for fast and robust tracking. Moreover, convex feasibility solvers allow for an efficient incorporation of context information and expert knowledge, and can provide robust results based on relatively small data sets. Our approach has numerous applications, including channel estimation, peak-to-average power ratio (PAPR) reduction in Orthogonal Frequency Division Multiplexing (OFDM) systems, radio map reconstruction, beam forming, localization, and interference reduction. We show that they can greatly benefit from the parallel architecture of GPUs.